Millions of public sector workers are set for an above-inflation pay rise due to be announced by Rachel Reeves next week after more than a decade of austerity.

The chancellor is expected to accept the recommendations of public sector pay bodies for pay increases on Monday – a move economists believe could cost up to £10bn.

The NHS and teaching pay bodies are reported to have recommended a 5.5% rise, and similar advice is likely to have been given by other pay review bodies, covering workforces such as doctors and dentists, armed forces, prisons and police officers.

The pay rises would help reverse years of declining wages, deal with staff shortages and see off the threat of industrial action.

Reeves is expected to confirm the increases as she sets out her case on Monday that the Conservatives left the government with a dire economic inheritance, including a black hole of £20bn.

Despite the difficult economic circumstances, she is expected to make the argument that the pay rises are necessary to avoid the costs to the economy seen in the waves of strike action under the Conservatives.

As part of the process, Reeves asked for an analysis from Treasury officials on the cost to the economy of industrial action, with the strikes of 2022 and 2023 having a knock-on impact on productivity.

This is understood to have found that every day of the teachers’ strikes cost the economy £300m because of lost working hours, while industrial action in the NHS cost £1.7bn in total to the taxpayer.

The cost of giving pay rises to public sector workers has not been fully budgeted for in current spending plans, but the money will have to be found through existing headroom, changes to fiscal rules or tax rises in the budget.

Before the election, Reeves had refused to say whether public sector workers would get a pay rise, saying she would need to look at the books before deciding.

But more recently, she hinted the government could be prepared to accept the advice of the pay bodies, saying there is “a cost to not settling” negotiations.

After a year of industrial action from 2022-23, most of the unions accepted pay deals with the Conservative government. However, Wes Streeting, the health secretary, is negotiating with junior doctors in an attempt to bring an end to their long-running industrial dispute.

Unions had warned of the likelihood of industrial action if the government were to ignore the advice of the independent pay review bodies.

Daniel Kebede, the general secretary of the National Education Union said last week: “It would be highly problematic for the Treasury to then intervene and then not implement a 5.5% pay award [if that is the recommendation].

“We absolutely would want to avoid strike action, but that would almost seem inevitable if the Treasury were to make such an intervention.”

In her statement to the House of Commons on Monday, Reeves will confirm the date of the budget, which is expected to be in the second half of October or November, and plans for a spending review.

She will also highlight some of the immediate pressures in areas such as the asylum system, prison places, welfare, defence and local council – and how the government intends to tackle them in the short term.

Economists have predicted Reeves will “kitchen sink” the bad news about the economy. The review is likely to conclude that existing spending plans are unsustainable and would require substantial cuts to public services, a position that economists had highlighted repeatedly before the election.

Presenting her Treasury audit to the Commons on Monday, the chancellor is expected to say her review has revealed state and privatised services are at risk of collapse under current plans.

Further billions are also committed in schemes like compensation for victims of the infected blood scandal and of the Horizon failures at the Post Office. The Cabinet Office minister, Nick Thomas-Symonds, told the House of Commons on Thursday that final compensation payments to patients infected with contaminated blood products and bereaved partners will begin to be made by the end of this year.

A higher than expected rise in public sector pay will put additional pressure on the public finances under Reeves’ self-imposed fiscal rules. The Institute for Fiscal Studies has estimated that if there were a 5.5% increase across all public sector professions, it would cost about £10bn.

Reeves has said the government will borrow only to invest within its fiscal rules, and that overall public debt should fall year-on-year as a share of gross domestic product by the fifth year of official forecasts.

Details of any taxation changes to meet the costs of extra public spending will not be outlined until the budget, but Reeves has little wriggle room having ruled out raising VAT, income tax or national insurance during the election.

The Guardian previously revealed in June that Labour has been drawing up options for raising wealth taxes. This includes a hike in capital gains tax (CGT) that could raise as much as £8bn.

Other changes being weighed include a rethink of inheritance tax that would require more stringent tests for “gifting” of assets such as farmland, which can currently be passed on tax free.

Added to the CGT changes, the measures together could raise more than £10bn. Draft analysis on the likely revenue raised and the consultation processes required were circulated among Labour insiders before election day and shared with senior government officials.

The head of Unite, Sharon Graham, has already been applying pressure on the government to change its fiscal rules so it can borrow more to invest in infrastructure and public services.

The union leader told Reeves that people “haven’t got time to wait for growth” after Labour put boosting economic output at the heart of its plans to repair the country’s finances.